Collaborations with Generative AI often begin with a short prompt and end with an opaque output, leaving implicit who was involved, what task was being pursued, which resources were used, and which constraints should have shaped the process. This limited contextual explicitness hinders trust, traceability, and accountability, particularly when Generative AI is embedded in information-intensive workflows such as search, querying, and profile management. This paper introduces From Prompts to Context, an ontology-driven framework for representing Human-Generative AI collaboration. Its core component, the Contextual Collaboration AI Ontology (CCAI), models key elements of collaboration - including tasks, agent roles, resources, and constraints - as a shared machine-interpretable vocabulary. By combining populated CCAI instances with SPARQL-based context retrieval in operational workflows, the framework turns otherwise ephemeral prompt-response interactions into structured and queryable collaboration traces linking prompts, outputs, and their surrounding context. The approach is illustrated through a case study involving a software development team building a competency-based education feature for viewing and updating learner competency profiles. The case study shows how the framework can support the representation and documentation of collaboration episodes across requirements analysis, design, implementation, and testing. Within this setting, the results indicate that explicit collaboration modelling helps make task context more explicit, improves the traceability of AI-generated contributions, and supports more transparent and accountable Human-Generative AI practices. We conclude by outlining design principles for future Human-Generative AI systems that emphasise not only output quality, but also the explicit representation of the collaborative context in which outputs are produced.

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